球面 CR 流形的 Kohn-Rossi 同调

IF 0.6 3区数学 Q3 MATHEMATICS

Annals of Global Analysis and Geometry Pub Date : 2024-03-30 DOI:10.1007/s10455-024-09952-1

Yuya Takeuchi

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引用次数: 0

摘要

摘要我们证明了一些球 CR 流形的 Kohn-Rossi 同调的消失定理。为此，我们使用了通过帕特森-沙利文度量定义的典范接触形式和 Kohn 拉普拉奇的 Weitzenböck 型公式。我们还发现，我们的结果在某些情况下是最优的。

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Kohn–Rossi cohomology of spherical CR manifolds

We prove some vanishing theorems for the Kohn–Rossi cohomology of some spherical CR manifolds. To this end, we use a canonical contact form defined via the Patterson–Sullivan measure and Weitzenböck-type formulae for the Kohn Laplacian. We also see that our results are optimal in some cases.

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来源期刊

Annals of Global Analysis and Geometry 数学-数学

CiteScore

1.20

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： This journal examines global problems of geometry and analysis as well as the interactions between these fields and their application to problems of theoretical physics. It contributes to an enlargement of the international exchange of research results in the field. The areas covered in Annals of Global Analysis and Geometry include: global analysis, differential geometry, complex manifolds and related results from complex analysis and algebraic geometry, Lie groups, Lie transformation groups and harmonic analysis, variational calculus, applications of differential geometry and global analysis to problems of theoretical physics.